There's something remarkable about a boat travelling uphill. Canal locks are a simple yet ingenious system that has made it possible for centuries.

The humble lock gate has more to it than first appears. Here's how one of the most common types works.

For a boat approaching a lock from below and meeting a closed gate:

Close the top gate to seal the lock. Then, open the sluice (or paddle) in the lower gate — often a sliding panel — by cranking it with the ever-handy windlass (a simple metal crank that fits onto square spindles on the lock mechanism).

Once the water is at the lower level, you can push the giant counterweights to open the gate and steer the boat inside. Don't nudge too far forward, or you'll bump the cill, a stone ledge at the top end of the lock. Close the gate behind you and shut the sluice to stop water escaping.

With the lock sealed, open the top sluices. These often feed through side channels or culverts, letting water in gently from upstream, usually below the surface, to reduce turbulence. You'll gradually float upward as the lock fills.

Once the water level matches the upper pound (the upper stretch of water), open the top gates, close the sluices, and cruise on your way.

The same principles, in reverse, work for approaching the lock from above.

As you can imagine, operating locks is much harder work if you're boating solo.

One thing that makes all this possible is a steady supply of water. You can't rise in a lock without water to fill it. So, canal builders had to ensure the canal had enough water to stay navigable and to keep the locks functioning.

For some of the London canals, the builders created huge reservoirs with long feeder channels to ensure the canals had enough water. In some places, water is pumped back uphill to be reused at the top of a flight.

Canal water doesn't flow much — it's a closed system in many places. I'd heard that, in principle, it only takes one lock's worth of water for a boat to travel down a whole flight of locks: each lockful of water carries the boat one step down and ends up in the next pound. So, a boat going down several locks essentially transfers a single chamber's worth of water from the top to the bottom.

But in practice, how much water gets used depends on boat traffic from either side, whether you meet locks full or empty, and water-saving features such as side pools. In my research, it wasn't as simple as it seemed.

Holding back tonnes of water is no small task. Mitre gates are angled to meet, pointing upstream and forming a shallow V. This shape means the water pressure pushes the gates closed, creating a tight seal — the water effectively locks itself in.

A stone arch bridge uses a similar principle—compression strengthens the structure under pressure.

Leonardo da Vinci sketched an early design for the mitre gate around 1500. The design still looks like a modern lock gate. Not bad for an invention 500+ years ago.

Canal locks are like playing with water in the bath but on a massive scale. They're inherently satisfying to watch and operate. At their peak, they revolutionised transport across much of Europe and beyond.

The same basic idea still operates in the Panama Canal, where giant ships are lifted 26 metres over the isthmus simply by filling and draining the lock chambers in sequence.

The dimensions of a lock determine the size of the boat that can pass through. Panamax is the maximum size a ship can be to fit through the Panama Canal—a constraint that shapes shipbuilding worldwide.

In the UK, Tardebigge Locks has 30 locks to raise boats 67m over just 3.6km. Not to be outdone, Caen Hill Locks on the Kennet and Avon Canal has 29 Locks, 16 of which are in a straight line, rising 72m over 2.1km.

We recently took a canal boat trip on London's Regents Canal, including a visit to London's Canal Museum.

Far from its industrial heyday, the whole place was buzzing with people out for leisure up and down the length of the journey. The towpath—horses towed the barges by walking alongside—was packed with walkers, joggers and cyclists.

And it never failed to fascinate when the boats moved up or down a lock.

Naismith's Rule (including the term "lock miles")

Canal Locks

Isometric projection is a simple way to draw 3D shapes. The meaning of isometric is "equal measure," from the Greek words iso- for equal and metric for measure. So, in an isometric drawing, all three axes, x, y, and z, are scaled equally, giving a clear, undistorted view of an object in three dimensions.

Except that isometric drawings can look a little odd and oversimplified. This is because of the lack of perspective, a visual distortion of 3D shapes we experience in the real world. In a perspective drawing, parallel lines converge in the distance towards a vanishing point, but in an isometric drawing, parallel lines stay parallel, and sizes don't get smaller in the distance.

The lack of perspective in an isometric view can make it look artificial, but it always looks clear.

I learned isometric drawing when studying engineering. Armed with a stack of isometric paper with a printed isometric grid, we had to reel off exercises involving drawing isometric views of 3D objects. And isometric projection is really handy for this. It can take a long time to build the skills to sketch a realistic 3D-looking object, perspective and all, but with isometric paper, you can quite quickly produce something that communicates to you or others what's in your head or on the workbench.

Isometric projection is handy for boxy shapes—I chose an approximation of the Bauhaus Dessau building by Walter Gropius to show it. If you need curves and angles, just like with perspective drawings, it can help to draw more boxes around these areas and use them to align your curves and meeting points for your lines.

Isometric views and their variations have had somewhat of a resurgence of late in video and board games. It turns out they're pretty helpful in map-based or city-building games such as Zynga's Farmville, Civilisation, or Sim City as the isometric view allows all parts of a scene to be viewed equally—in the distance or up close—while still seeing every detail in, say, a building, wherever it is.

If you want to try some isometric drawings, making your own isometric grid paper is easy. Just draw equally-spaced vertical stripes and then a criss-cross of lines in both directions at 30 degrees from the horizontal. This gives a host of equilateral triangles and an easy base to start drawing your 3D objects. Or just download some templates online. You'll find that building up more complex shapes out of cubes is dead simple if you keep to the lines on the isometric grid.

Just as in the drawing here, sometimes shapes drawn in isometric view lend themselves to curious optical effects. The lack of perspective can make the difference between heights and depths ambiguous. So, you can't always tell if two surfaces are at very different heights or if one is in the distance. The brilliant puzzle game Monument Valley uses this quirk of isometric projection to create mind-bending puzzles that are well worth a try. For instance, rotating a high surface can suddenly make a platform that extends far into the distance 🤯.

Isometric-like projection can also help make impossible shapes, such as the Impossible Staircase, or Penrose stairs. Another type of projection, anamorphosis, creates a drawing that only looks correct from a particular viewpoint. Anamorphosis leads to some remarkable street art.

2.5D objects, including an old video of me drawing a sketchplanation

The Impossible Staircase, or Penrose stairs

When drawn nice and faint, the isometric grid is an example of a ghost grid

Isometric projection is quite the opposite of "draw what you see, not what you think." Foreshortening can be hard to get the hang of.

Isometric projection

It's mindblowing to me to think at any moment, over 6,000 satellites are whipping around the Earth at terrific speeds and somehow not drifting off into space or crashing into Earth. How does this work?

An orbit around Earth is a delicate balance between the momentum of a satellite traveling at speed parallel to the Earth's surface and the constant tug of gravity towards the Earth.

If the satellite travels too slowly, gravity wins, eventually pulling the satellite back to Earth. If it travels too fast, gravity isn't strong enough to hold it, and the satellite will shoot off into space. But at just the right speed—which depends on its distance from Earth—gravity will pull the satellite towards Earth, but the satellite's speed ensures it will keep missing and instead continue its journey orbiting around Earth. In this case, gravity acts as a centripetal force, a force acting towards the centre, enabling satellites to stay in orbit.

Newton had a thought experiment known as Newton's Cannon where he imagined firing a cannonball off a high mountain at different velocities and what the resultant trajectories would be.

Most orbits are slightly elliptical or oval-shaped. For example, the elliptical nature of the Moon's orbit gives us the joys of things like supermoons.

Orbit

The Swiss Cheese Model helps explain why, despite all our best intentions, accidents happen.

Analysis of accidents in large complex systems such as power stations or plane crashes led to an understanding that "no one failure, human or technical, is sufficient to cause an accident. Rather, it involves the unlikely and often unforeseeable conjunction of several contributing factors arising from different levels of the system."

James Reason's Swiss Cheese Model is a memorable visual metaphor that illustrates how each safeguard may contain a latent flaw or hole and that an unfortunate circumstance may result in these holes lining up to disastrous effect. It's also a nice reminder that multiple layers of defence will be more effective, but even with our best efforts, there's still potential for something to go wrong.

Excerpt from Revisiting the "Swiss Cheese" Model of Accidents (pdf), Reason, Hollnagel and Paries, 2006.

Coronavirus example from the Cleveland Clinic.

I learned recently that it's sometimes called the "cumulative act effect".

This sketch, updated and polished, features with a number of others in my book Big Ideas Little Pictures.

The Swiss Cheese Model

Jevon's Paradox is the counterintuitive idea that improvements in fuel efficiency tend to increase, rather than decrease, overall fuel use.

In 1865, William Stanley Jevons, a British economist, observed that despite significant improvements in coal efficiency in steam engines, total coal consumption actually rose. Rather than saving fuel, efficiency made coal-powered energy more economical, driving increased industrial use. This observation became known as Jevon's Paradox.

Though first identified towards the end of the Industrial Revolution, Jevon's Paradox is still highly relevant today, particularly in discussions around energy efficiency, sustainability, and technology.

Fuel-efficient cars – When vehicles become more fuel-efficient, the cost per mile driven decreases. As a result, people tend to drive more, offsetting the efficiency gains.

AI and computing power – Advances in AI and computing efficiency reduce the cost of processing power, leading to increased overall usage of AI models and cloud computing.

Battery technology – More efficient batteries lead to the proliferation of battery-powered devices rather than reducing energy consumption.

Water-saving devices – Low-flow showerheads and toilets may save water per use, but in some cases, they lead to longer showers or more frequent flushing.

Lighting — Though LED lights are vastly more efficient than their predecessors, we are continually finding new ways to use our low-wattage lights that we had never dreamed of before.

Household appliances – In her book More Work for Mother, Ruth Cowan addresses the ironies of household appliances, such as washing machines and vacuum cleaners, and how improvements in efficiency often led to more work through more frequent washing, not less.

This tendency is sometimes referred to as the rebound effect, where changes in behaviour partially or fully cancel out expected energy or resource savings.

With the rise of AI and automation, Jevon's Paradox is playing out again in new ways:

Computational efficiency – Though AI models are becoming more efficient—DeepSeek a case in point—the demand for AI-generated content, large language models, and deep learning applications is growing rapidly.

Automated processes – Instead of reducing overall workloads, automation often leads to more tasks being completed rather than fewer tasks needing to be done.

Cloud computing – More efficient data centres have not reduced overall energy use because the demand for cloud services and machine learning applications continues to skyrocket.

Understanding Jevon's Paradox can help in designing better policies and strategies to ensure efficiency gains lead to real reductions in resource consumption. Some approaches include:

Carbon pricing and regulation – Ensuring that energy efficiency is paired with policies that discourage excessive consumption. (see Goodhart's Law)

Shifting behaviors – Encouraging individuals and businesses to actively reduce energy use, rather than simply taking advantage of efficiency improvements.

Technology with constraints – Implementing smart grid systems, time-based energy pricing, and consumption limits to prevent unchecked increases in demand.

Jevon's Paradox reminds us that efficiency alone is not a guaranteed solution for reducing resource consumption. Instead, it often requires complementary policies, incentives, and behavior changes to make efficiency gains truly effective.

The Automation Paradox – The better the machines get, the more we struggle when they fail

Wishcycling — Hoping something can be recycled

Save some landfill with reusable diapers/nappies

Jevon’s Paradox

In my everyday life I’d have been hard pushed to put my finger on the difference between accuracy and precision but, in engineering at least, you learn that there is a clear difference between the two.

Precision describes how variable an outcome is, or how close repeated measurements or actions are to each other.

In contrast, something may be very precise but not be accurate to your intent or to the true value of a thing. That’s accuracy — how close you are to the true or intended value. If you’re hitting near your intended target then you’re accurate.

Hmm…one of those things where a sketchplanation works a whole lot better than words.

For the more spiritually inclined: Everything is aiming

Or for the more statistically inclined: Measures of central tendency (mean, median, mode), and Common distributions (normal, skewed, pareto)

That accuracy is true to intention and precision true to itself, I learned from Simon Winchester in Exactly: How precision engineers created the Modern World.

Accuracy and precision

Rubberducking is a problem-solving technique where you explain your code or task to a rubber duck—or any inanimate object—and discover the solution yourself through the act of explaining. It's brilliant because it works and is effectively free.

Rubberducking, or rubber ducking, is most commonly associated with debugging in software development but can be applied to any problem-solving process.

The name comes from the book The Pragmatic Programmer by Andrew Hunt and David Thomas. In it, the authors suggest using a rubber duck as a conversation partner to clarify one’s thoughts. This is an accessible and effective way to troubleshoot problems without requiring someone else’s time.

Have you ever been called over to someone’s desk to help them solve a problem, and as they explain the problem to you or demonstrate it, they figure out the answer themselves? It happens all the time to me, particularly when someone's showing me how something doesn't work, and it magically works just by having me watch over their shoulder.

The rubber duck technique is as simple as that, except that instead of calling someone over, you can simply replace the person with a rubber duck, teddy bear or heck, even your stapler.

The psychology behind rubberducking relies on how explaining a problem forces you to process your thoughts more clearly, often revealing gaps or errors in your understanding. Here’s how you can try it yourself:

1. Set up your “duck”: Place a rubber duck, teddy bear, or any object on your desk.

2. Explain your problem: Describe your code, logic, or issue to the duck, step by step, as if you’re teaching it.

3. Watch for insights: In explaining it aloud, you’ll often uncover what’s wrong or identify a new approach to solving it.

For example, a developer struggling with a bug might explain every line of code to the duck. Verbalising their logic can highlight an overlooked detail that resolves the problem.

Rubberducking works because it forces you to articulate your thoughts clearly, moving them from abstract notions in your head to concrete statements. This shift can:

• Help you identify assumptions you didn’t realise you were making.

• Mimic the process of pair programming without needing another person.

Rubberducking a problem also reduces dependency on others for problem-solving, making it a cost-effective—basically free!—and time-efficient tool for debugging.

Here are some situations where it’s particularly useful:

• Debugging code: Talk through an error or bug in your program.

• Explaining logic: Test the clarity of your solution by explaining it step by step.

• Learning new concepts: Summarise a concept to the duck to check your understanding (see the Feynman Learning Technique)

• Decision-making: Walk through the pros and cons of a decision.

In software development, rubber duck debugging has become a recognised term for this process. It’s so common that some developers keep an actual rubber duck on their desks to symbolise this practice. Teams might 'joke' about needing “a duck” for the simplest bugs.

Debugging is an integral part of coding, and the rubber duck technique makes it less daunting. By verbalising your thought process, you streamline problem-solving without needing external help.

Frequently Asked Questions about Rubberducking

Nope. While a rubber duck is the classic choice, you can use anything nearby—your coffee cup, a stapler, or even a photo on your desk.

Q: What if talking out loud isn’t possible?

Writing out your explanation or saying it in your head can work just as well. The key is clarifying and articulating your thought process.

Q: How is this different from pair programming?

Pair programming involves working alongside another person on the same task. Some people swear by pair programming, and to be honest, I've always found it effective whenever I try it. However, rubberducking is a solo activity where the act of explanation itself is the solution.

Next time you're stuck on something, grab a rubber duck and give it a try.

Rubberducking is similar to the empty chair technique for psychotherapy, which involves speaking to an empty chair as if addressing a person.

It's also easily confused with "rubbernecking," which is slowing down to look at an accident as you drive past—a common cause of traffic jams.

What is Rubberducking? An Explanation of the Rubber Duck Debugging Technique

Orthographic projection is a handy technique for communicating much of what you need about something. In an orthographic drawing, you draw a face-on, side-on, and top-down view of an object, allowing you to see the same shape from different perspectives in a single drawing.

The neat thing I found about an orthographic drawing is how, when laid out as in the sketch, the dimensions of one view can be extended into the adjacent views, helping to keep the drawing accurate. I definitely felt some satisfaction and enjoyment working on an orthographic projection drawing on a large drawing board with a built-in ruler.

While orthographic projections can be helpful for accurately representing an object, they struggle a bit with hollows and some other features that can make them start to look a bit fiddly.

Perhaps combine an orthographic view with an isometric projection.

Orthographic projection

A way of helping decide what to do next based on Must do, Should do, Could do and Would do.

Strangely, so many of the things you’d really like to do when put in this organisation end up in the Would bucket.

MOSCOW Prioritisation.

The piston is an amazingly simple, ridiculously useful and successful mechanism that, together with a connecting rod and crankshaft, converts linear motion to rotational motion.

This simple system is basically what allows us to take a force produced by, say, steam or an explosion and make a wheel turn. Stick a few of these together and time the rotation of each correctly, carefully controlling the explosions and the exhaust, and you have an internal combustion engine that powers and moves our cars.

There are a lot of amazing things to me about it, but I am still impressed with how effectively it takes something moving back and forth and makes something spin around and vice versa.

The piston

A 2.5D shape is three-dimensional, but the use of the third dimension, usually height, is limited to simple top-down operations. I learned about 2.5D, or two and a half dimensions, from my engineering days.

It turns out it’s really quite common to make 2.5D things because, for example, it’s easy to drill or mill down into something, and it's a pain to turn something on its side and drill from the other side. Or, as with vacuum forming, it’s easy to suck plastic onto a mold but a pain to get it off if you’ve got any overhangs as you can’t lift it straight up again. Hence, the plastic sandpit in our garden is a 2.5D object rather than true 3D.

As we become more sophisticated at making things, more objects will be true 3D rather than 2.5D. But the simple two-and-a-half-dimensional option is still generally cheaper and easier and will not disappear soon.

Civilization, in general, looks rather 2.5D from the air as we tend to build upwards, but we don’t find overhangs that easy or practical, thanks also to gravity, e.g., the Pyramids.

I recorded a video of the drawing of this sketch. Watch making a sketchplanation—2.5D

2.5D

The International Load Line, formerly called the Plimsoll Line, is an internationally adopted system for ensuring ships aren’t overloaded. Safe loading levels vary depending on the salinity—how salty it is—and the temperature of the water.

The Plimsoll line

The idea of resolving contradictions I was taught by Darrell Mann. This neat example from Simon Dewulf.

Engineering sketches